Final answer:
The contribution margin ratio for Duck Manufacturing is calculated by determining the contribution margin per unit, which is then divided by the selling price per unit. After calculating, it is found to be 38.5%, rounded to the nearest tenth. Option b
Step-by-step explanation:
To calculate the contribution margin ratio for Duck Manufacturing, we first need to determine the contribution margin per unit. This is the selling price per unit minus the variable cost per unit. However, since the variable cost per unit is not provided directly, we calculate it based on the break-even point. At the break-even point, total revenue equals total costs (which is the sum of fixed costs and variable costs).
We are given that Duck Manufacturing sells each pair of boots for $52 and must sell 18,000 pairs to break even. This implies a total revenue at break-even point of $52 × 18,000 = $936,000. Given that the fixed costs are $360,000, we can calculate the total variable costs at break-even by subtracting fixed costs from total revenue, which is $936,000 - $360,000 = $576,000. So the variable cost per unit is $576,000 / 18,000 = $32 per pair.
Now, the contribution margin per pair is the selling price per pair ($52) minus the variable cost per pair ($32), resulting in a contribution margin of $20 per pair. The contribution margin ratio is then contribution margin per pair divided by the selling price per pair: $20 / $52 = 0.3846 or 38.5% when rounded to the nearest tenth.
To visually represent this:
Selling price per unit (P): $52
Total units for break-even (Q): 18,000
Total fixed costs (FC): $360,000
Total revenue at break-even (TR): P * Q = $52 * 18,000 = $936,000
Total variable costs at break-even (TVC): TR - FC = $936,000 - $360,000
Variable cost per unit (VC): TVC / Q = $576,000 / 18,000
Contribution margin per unit (CM): P - VC = $52 - $32
Contribution margin ratio (CM ratio): CM / P = $20 / $52. Option b